Just get a 55-250 IS.
It should be fine during the day!
How often do you go to the zoo?
I have a 70-200 f/4 IS and it, too, is nice, but it will cost you. I have a Family membership at my local zoo, and I guess I'm tired of bringing my 70-200. I just throw my 55-250 IS in my pocket, which provides adequate snapshots if I need telezoom. Zoo animals don't run fast if you are worried about focusing.
Now, if you intend to sell your pics, or have plans for other shoots (sports, portraits) then go for the "L's."
I don't think a prime is good fo zoos. They're very limiting.
I'd use the rest of the money you plan to spend on a lens you would use more often like a 17-55 IS. I don't have one, but I do use a 17-50 Tammy, and at times I wish I had IS.